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<a href="_math_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment"> * </span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> *</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> * \brief       Very basic math abstraction layer.</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> * </span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> * \par</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> * This file serves as a minimal abstraction layer.</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> * Inclusion of this file makes some frequently used</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> * functions, constants, and header file inclusions</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> * OS-, compiler-, and version-independent.</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> * </span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> * </span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> * </span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> *</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> * \author      -</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * \date        -</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> *</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> *</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * </span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * </span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published </span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> * </span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span><span class="comment"> * </span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="comment"> *</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span><span class="comment"> */</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span><span class="preprocessor">#ifndef SHARK_CORE_MATH_H</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="preprocessor">#define SHARK_CORE_MATH_H</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span> </div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="preprocessor">#include &lt;boost/math/constants/constants.hpp&gt;</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="preprocessor">#include &lt;boost/math/special_functions/sign.hpp&gt;</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="preprocessor">#include &lt;boost/utility/enable_if.hpp&gt;</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span><span class="preprocessor">#include &lt;limits&gt;</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span><span class="preprocessor">#include &lt;type_traits&gt;</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span><span class="preprocessor">#include &lt;<a class="code" href="_exception_8h.html">shark/Core/Exception.h</a>&gt;</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span> </div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a> {</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <span class="comment">// define doxygen group for shark global functions, var, etc. (should only appear once in all shark files)</span><span class="comment"></span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span><span class="comment">    /**</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span><span class="comment">    * \defgroup shark_globals shark_globals</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span><span class="comment">    * </span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span><span class="comment">    * \brief Several mathematical, linear-algebra, or other functions within Shark are not part of any particular class. They are collected here in the doxygen group &quot;shark_globals&quot;</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span><span class="comment">    * </span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span><span class="comment">    * @{</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span><span class="comment">    *</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span><span class="comment">    */</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="comment"></span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span><span class="comment">    /**</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span><span class="comment">    * \brief Constant for sqrt( 2 * pi ).</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span><span class="comment">    */</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"><a class="line" href="group__shark__globals.html#ga49b759f4712477bf89276a6c944fec47">   65</a></span>    <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="group__shark__globals.html#ga49b759f4712477bf89276a6c944fec47" title="Constant for sqrt( 2 * pi ).">SQRT_2_PI</a> = boost::math::constants::root_two_pi&lt;double&gt;();</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span><span class="comment">//  static const double SQRT_PI = boost::math::constants::root_pi&lt;double&gt;();</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="comment"></span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span><span class="comment">    /// Maximum allowed input value for exp.</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> T&gt;</div>
<div class="foldopen" id="foldopen00070" data-start="{" data-end="}">
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"><a class="line" href="group__shark__globals.html#ga243e2255f50ad695bf9d2b1bf46d5b92">   70</a></span>    T <a class="code hl_function" href="group__shark__globals.html#ga243e2255f50ad695bf9d2b1bf46d5b92" title="Maximum allowed input value for exp.">maxExpInput</a>(){</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        <span class="keywordflow">return</span> boost::math::constants::ln_two&lt;T&gt;()*std::numeric_limits&lt;T&gt;::max_exponent;</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    }<span class="comment"></span></div>
</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span><span class="comment">    /// Minimum value for exp(x) allowed so that it is not 0.</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> T&gt;</div>
<div class="foldopen" id="foldopen00075" data-start="{" data-end="}">
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"><a class="line" href="group__shark__globals.html#ga3803cedc2acd6e2bcd5a5bc53765d5e4">   75</a></span>    T <a class="code hl_function" href="group__shark__globals.html#ga3803cedc2acd6e2bcd5a5bc53765d5e4" title="Minimum value for exp(x) allowed so that it is not 0.">minExpInput</a>(){</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        <span class="keywordflow">return</span> boost::math::constants::ln_two&lt;T&gt;()*std::numeric_limits&lt;T&gt;::min_exponent;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    }</div>
</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span><span class="comment"></span> </div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span><span class="comment">    /// Calculates x^2.</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span><span class="comment"></span>    <span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt; </div>
<div class="foldopen" id="foldopen00081" data-start="{" data-end="}">
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"><a class="line" href="group__shark__globals.html#gae1f82613484173e9fe1a07960dabff63">   81</a></span>    <span class="keyword">inline</span> <span class="keyword">typename</span> boost::enable_if&lt;std::is_arithmetic&lt;T&gt;, T&gt;::type <a class="code hl_function" href="group__shark__globals.html#gae1f82613484173e9fe1a07960dabff63" title="Calculates x^2.">sqr</a>( <span class="keyword">const</span> T &amp; x) {</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        <span class="keywordflow">return</span> x * x;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    }</div>
</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span><span class="comment"></span> </div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span><span class="comment">    /// Calculates x^3.</span></div>
<div class="foldopen" id="foldopen00086" data-start="{" data-end="}">
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"><a class="line" href="group__shark__globals.html#ga7bcf4b76ebc11e508c922d7aa05c729b">   86</a></span><span class="comment"></span>    <span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt; <span class="keyword">inline</span> T <a class="code hl_function" href="group__shark__globals.html#ga7bcf4b76ebc11e508c922d7aa05c729b" title="Calculates x^3.">cube</a>( <span class="keyword">const</span> T &amp; x) {</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        <span class="keywordflow">return</span> x * x * x;</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    }</div>
</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    <span class="comment"></span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span><span class="comment">    ///\brief Logistic function/logistic function.</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span><span class="comment">    ///Calculates the sigmoid function 1/(1+exp(-x)). The type must be arithmetic. For example</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span><span class="comment">    ///float,double,long double, int,... but no custom Type. </span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> T&gt;</div>
<div class="foldopen" id="foldopen00095" data-start="{" data-end="}">
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"><a class="line" href="group__shark__globals.html#ga28f3c1d61cf1c070d4687d03bc5d99e9">   95</a></span>    <span class="keyword">typename</span> boost::enable_if&lt;std::is_arithmetic&lt;T&gt;, T&gt;::type <a class="code hl_function" href="group__shark__globals.html#ga28f3c1d61cf1c070d4687d03bc5d99e9" title="Logistic function/logistic function.">sigmoid</a>(T x){</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        <span class="keywordflow">if</span>(x &lt; minExpInput&lt;T&gt;()) {</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>            <span class="keywordflow">return</span> 1;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>        }</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        <span class="keywordflow">if</span>(x &gt; maxExpInput&lt;T&gt;()) {</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>            <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>        }</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        <span class="keywordflow">return</span> 1. / (1.+ std::exp(-x));</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    }</div>
</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <span class="comment"></span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span><span class="comment">    ///\brief Thresholded exp function, over- and underflow safe.</span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span><span class="comment">    ///Replaces the value of exp(x) for numerical reasons by the a threshold value if it gets too large.</span></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span><span class="comment">    ///Use it only, if there is no other way to get the function stable!</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span><span class="comment">    ///@param x the exponent</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> T&gt;</div>
<div class="foldopen" id="foldopen00112" data-start="{" data-end="}">
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"><a class="line" href="group__shark__globals.html#gae47c137a0eb0ef64df529df43c456d15">  112</a></span>    T <a class="code hl_function" href="group__shark__globals.html#gae47c137a0eb0ef64df529df43c456d15" title="Thresholded exp function, over- and underflow safe.">safeExp</a>(T x ){</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        <span class="keywordflow">if</span>(x &gt; maxExpInput&lt;T&gt;()){</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>            <span class="comment">//std::cout&lt;&lt;&quot;warning, x too high&quot;&lt;&lt;std::endl;</span></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>            <span class="keywordflow">return</span> 0.9 * std::numeric_limits&lt;long double&gt;::max();</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        }</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        <span class="comment">//Allow Koenig Lookup</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        <span class="keyword">using </span>std::exp;</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        <span class="keywordflow">return</span>  exp(x);</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    }<span class="comment"></span></div>
</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span><span class="comment">    ///\brief Thresholded log function, over- and underflow safe.</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span><span class="comment">    ///Replaces the value of log(x) for numerical reasons by the a threshold value if it gets too low.</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span><span class="comment">    ///Use it only, if there is no other way to get the function stable!</span></div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span><span class="comment">    ///@param x the exponent</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> T&gt;</div>
<div class="foldopen" id="foldopen00127" data-start="{" data-end="}">
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"><a class="line" href="group__shark__globals.html#gafa0dd39814ad67a0cbba4b0d0e5308b2">  127</a></span>    T <a class="code hl_function" href="group__shark__globals.html#gafa0dd39814ad67a0cbba4b0d0e5308b2" title="Thresholded log function, over- and underflow safe.">safeLog</a>(T x)</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    {</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        </div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>        <span class="keywordflow">if</span>(x&gt; -std::numeric_limits&lt;T&gt;::epsilon()  &amp;&amp; x &lt; std::numeric_limits&lt;T&gt;::epsilon()){</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>            <span class="comment">//std::cout&lt;&lt;&quot;warning, x too low&quot;&lt;&lt;std::endl;</span></div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>            <span class="keywordflow">return</span> boost::math::sign(x)*std::numeric_limits&lt;T&gt;::min_exponent;</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        }</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>        </div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        <span class="comment">//Allow Koenig Lookup</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        <span class="keyword">using </span>std::log;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        <span class="keywordflow">return</span> log(x);</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    };</div>
</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    <span class="comment"></span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span><span class="comment">    ///\brief Numerically stable version of the function log(1+exp(x)).</span></div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span><span class="comment">    ///Numerically stable version of the function log(1+exp(x)).</span></div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span><span class="comment">    ///This function is the integral of the famous sigmoid function.</span></div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span><span class="comment">    ///The type must be arithmetic. For example</span></div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span><span class="comment">    ///float,double,long double, int,... but no custom Type. </span></div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> T&gt;</div>
<div class="foldopen" id="foldopen00147" data-start="{" data-end="}">
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"><a class="line" href="group__shark__globals.html#gac93b0b1252780b58f096ce0eb6065273">  147</a></span>    <span class="keyword">typename</span> boost::enable_if&lt;std::is_arithmetic&lt;T&gt;, T&gt;::type <a class="code hl_function" href="group__shark__globals.html#gac93b0b1252780b58f096ce0eb6065273" title="Numerically stable version of the function log(1+exp(x)).">softPlus</a>(T x){</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        <span class="keywordflow">if</span>(x &gt; maxExpInput&lt;T&gt;()){</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>            <span class="keywordflow">return</span> x;</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>        }</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        <span class="keywordflow">if</span>(x &lt; minExpInput&lt;T&gt;()){</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>            <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        }</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>        <span class="keywordflow">return</span> std::log(1+std::exp(x));</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    }</div>
</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    <span class="comment"></span></div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span><span class="comment">    ///\brief Numerically stable version of the function log(1+exp(x)). calculated with float precision to save some time</span></div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span><span class="comment">    ///Numerically stable version of the function log(1+exp(x)).</span></div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span><span class="comment">    ///This function is the integral of the famous sigmoid function.</span></div>
<div class="foldopen" id="foldopen00161" data-start="{" data-end="}">
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"><a class="line" href="group__shark__globals.html#ga663a0f23602a6a81bfad2694785868a1">  161</a></span><span class="comment"></span>    <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code hl_function" href="group__shark__globals.html#gac93b0b1252780b58f096ce0eb6065273" title="Numerically stable version of the function log(1+exp(x)).">softPlus</a>(<span class="keywordtype">double</span> x){</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>        <span class="keywordflow">if</span>(x &gt; 15){</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>            <span class="keywordflow">return</span> x;</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>        }</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>        <span class="keywordflow">if</span>(x &lt; -17){</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>            <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        }</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>        <span class="keywordflow">return</span> std::log(1.0f+std::exp(<span class="keywordtype">float</span>(x)));</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    }</div>
</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    <span class="comment"></span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span><span class="comment">    ///brief lets x have the same sign as y.</span></div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span><span class="comment">    ///This is the famous well known copysign function from fortran.</span></div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> T&gt;</div>
<div class="foldopen" id="foldopen00175" data-start="{" data-end="}">
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"><a class="line" href="group__shark__globals.html#gaea90fc4ad82597d2324042c4990b4207">  175</a></span>    T <a class="code hl_function" href="group__shark__globals.html#gaea90fc4ad82597d2324042c4990b4207">copySign</a>(T x, T y){</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>        <span class="keyword">using </span>std::abs;</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        <span class="keywordflow">if</span>(y &gt; 0){</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>            <span class="keywordflow">return</span> abs(x);</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>        }</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        <span class="keywordflow">return</span> -abs(x);</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>    }</div>
</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>}</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span> </div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span><span class="preprocessor">#endif </span></div>
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